1.1 Motivation

The rigidity of the dome enabled early builders to achieve large spans with a material of minimal tension capacity. The strength inherent in the doubly curved dome, arising from the interlocking of multiple arches, has resulted in many culturally significant monuments throughout history. The structural performance of the masonry dome under challenging loading conditions has inspired many architects, builders and structural engineers.

Rafael Guastavino exploited the properties of the dome with a proprietary system that he called ‘cohesive construction.’ Although the capabilities of this construction system enabled the realization of many important buildings between the 1890s and 1940s in North America, this system is a lost art today. It is the intention of this study to further the understanding and appreciation of Guastavino domes. In this respect, the study will clarify unanswered or inadequately answered questions about the structural behavior of the domes built using this technique.

The domes of the present also stand to benefit from further studies of the behavior of the spherical thin shells of past. A study of the structural principles and architectural applications of Guastavino domes may also provide insight into the analysis of domes in contemporary engineering. Only by fully comprehending historic domes can we ensure our ability to design and execute improved domed structures in the future.

1.2 Background

Finite element analysis (FEA) is a widely used method to assess the mechanical behavior of a variety of structural systems. In applications of FEA, various assumptions are necessary for the sake of simplification or reduction of the problem scope. Many of these assumptions are developed from the analyst’s understanding of the structure’s behavior. The success and accuracy of an FE model is dependent on the correctness of these assumptions. A search for a means to verify the correct representation of the structural behavior of the system in an FE model has been addressed in many applications. In early attempts, the judgment of the validity of an FE model was assessed according to the correlation of FEA estimates with classical analytical solutions. Recently, with the rapid development in experimental techniques–particularly in experimental modal analysis–this validation can be accomplished by comparisons of the FEA estimates to experimental data. Moreover, model-updating procedures are developed to iteratively modify the variables of an FE model in order to correlate with the experimental data.

The application of FEA to hemispherical shells has been addressed widely in literature. Some studies have overlooked the verification of the created model, while others have used validation methods ranging from entirely theoretical efforts to experimental testing procedures. When experimental validation procedures are discussed, various hemispherical shell specimens are studied under controlled conditions.  In essence, the authors are able to employ both analytical and experimental methods to achieve good correlation. The validation studies in these works focused on small scale, experimentally constructed, homogenous laboratory specimens.

Other studies have also adopted FEA in the assessment of the behavior of existing masonry structures. Various efforts have been published addressing the potential uncertainties in an FE model while attempting to provide a measure to check the accuracy of the FEA solution for masonry structures. Among these studies, the initial model validation attempts are limited to visual comparisons of the tension zones in the FEA solution with the existing cracks on the masonry structure. Two other methods employed in the assessment of the structural behavior of existing masonry structures involved experimentally measuring the stress by means of strain gauges and destructive tests which load up the structure to collapse. The combination of spherical shells and existing masonry buildings–masonry domes–has not gone unnoticed. The development of analytical formulas for masonry domes dates back to the 18^th century.  Three centuries later, numerous publications regarding the static and dynamic solutions of domes in all kinds of geometry, varying from spherical to elliptical, are available in literature.

1.3 Problem Statement and Proposed Study

Although a significant amount of analytical research has been done on masonry domes, there is no study providing either an experimental or analytical validation procedure in order to eliminate the uncertainties in modeling for masonry domes. This research aims to fill this gap by addressing three distinct problems:

• Structural Analysis: The conventional application of FEA to existing masonry buildings introduces many assumptions and simplifications due to numerous unknown factors. While large scale masonry structures are of primary concern, techniques of finite element modeling and its solutions are reliable only when the analytical model is validated. Successful replication of boundary conditions has been a particularly challenging task in all FEA practices, since it is mainly reliant on the analyst’s understanding and often involves over-simplification of the support conditions. In addition, limited knowledge of actual material properties and the unknown shell thickness in historic domes may increase the uncertainty in FEA solutions. In many cases, historic masonry structures include ornamentation as a part of the structural system, so it is hard to simplify the structure during geometric model creation.  Since there is no predetermined level for simplification, this factor is also dependent on the analyst’s intuition. Validation of the material properties, shell thickness, and boundary conditions of the mathematical FE model, as well as the verification of the assumptions and geometric simplifications, are essential for the successful prediction of the structural behavior of a masonry dome. This research addresses an experimental approach to reduce the uncertainties in the FEA model caused by unknown factors of historic large-scale masonry shells and provides a process that can be followed in future studies.
• Experimental Analysis: In this research, we will develop a non-destructive testing protocol for full-scale masonry domes. Since each experimental case poses its own potential problems and challenges to reach a reliable outcome, the establishment of user preferences for the experimental variables is important to this study. This research provides a non-destructive testing guide for masonry domes by presenting solutions developed for the problems encountered during testing, as well as by identifying user preferences during test set-up for existing masonry domes.
• Architectural History: The topic of the Guastavino vaulting system has inspired a large amount of writing. Despite the substantial number of Master’s level studies published on the preservation issues and on the history of the development of this technique, the structural issues posed by this system have received less attention. Almost all of the publications, however, comment on the structural capabilities of the Guastavino brand of vaulting without completing an in-depth structural analysis on the existing examples.

A number of scholars have recognized the “cohesive construction” technique of Guastavino as an early application leading to today’s thin elastic shell structures. This study presents a basis for the discussion of the claims of Guastavino and later researchers that the strength of this construction type results from the “cohesion” (development of tensile stresses) in the material. This study also aims to identify the extent of the inherent elasticity in this brand of domes. Known as a successful marketer, Guastavino originated many claims for “cohesive construction.” His sayings were accepted and praised by some, while others argued for the opposite. A particularly pervasive argument of Guastavino that is widely accepted by historians is that ‘cohesive domes do not exert thrust on their supports.’ This claim in particular is investigated in this study.

1.4 Scope of Research

This research intends to provide a thorough analysis of the structural behavior of Guastavino tile domes by means of a complete study. This can only be achieved through an evaluation of the existing examples. The problems listed above are addressed with the use of experimental modal analysis, impact-echo techniques, experimental stress analysis, thin elastic shell theory and finite element analysis applications.

These tasks are applied to two existing masonry domes built by the Guastavino Fireproof Company. Both of the domes are built in the cohesive construction system, with 1” thick tiles laid flat and bedded in Portland cement mortar with staggered joints between adjacent layers. A discussion on ‘cohesive construction’ is provided in Chapter 6, while brief descriptions of the structures are provided in following paragraphs.

• City County Building (CCB) – Pittsburgh, PA
  The City County Building has three identical Guastavino tile domes of 6.7 m radius that span over the entrance vestibule. The pendentives and massive arches support the highly ornamented domes, which are constructed with a varying thickness of three to seven tiles [Figure 1-1].
• State Education Building (SEB) – Albany, NY
  In the State Education Building, twelve identical rib and dome constructions are arranged in a three by four grid. This arrangement creates a repetitive circular system reminiscent of Labrouste’s Bibliothèque Nationale in Paris (Parks 1996). In the SEB, slender iron columns support the repeated system of Guastavino tile domes of 6.7 m radius. The transformation from a circular plan to a square bay is accomplished by means of pendentives and slender ribbed arches [Figure 1-2].
  

1.5 Objectives of Research

This research, addressing three distinct objectives, provides sufficient information for the extrapolation of the described methodologies to other masonry-domed structures. The objectives of this study are listed below [Figure 1-3].

1. Experimentally determine the dynamic characteristics of the structures under study.
2. Develop a validated finite element model of the structures under consideration by the commercially available FEA program ANSYS.
3. Examine the structural characteristics of Guastavino tile domes and appraise the available information on the structural capabilities of this type of vaulting.

1.6 Concluding Remarks

To achieve the objectives described above, two existing Guastavino domes are analytically modeled and experimentally tested in order to make inferences about the structural behavior of masonry domes and the relationship between their structural integrity and the architectural context.

For these purposes, this research presents the use of experimental modal analysis to calibrate the analytical solutions and describes the essentials of this non-destructive approach for historic masonry domes. A testing procedure for masonry domes is developed, and the particulars of the experiments, as applied to masonry domes, are provided. Additionally, the techniques of impact-echo are utilized to determine the unknown dome shell thickness experimentally.

The general differential equations of thin shell theory are adapted to the structures studied. By this method, axisymmetric mode shapes are obtained for comparison with FE model predictions and experimental data.

The solution of the problems in structural analysis is achieved by assuring that the proposed FE model correctly represents the experimentally determined mode shapes. The numerical comparison of natural frequencies and visual comparisons of mode shapes are used to validate the FE model.

The structural assessment of the Guastavino tile domes is achieved by examining the static state of stress and reaction forces. The validated FE models are used to investigate the importance of hoop tension under gravity loading. According to the comparisons of FE results with the current conditions of the structures, the elastic or inelastic behavior of Guastavino domes is revealed.

Based on the findings of the present research and the available literature on the topic, this thesis finally presents a discussion on specific issues regarding the structural behavior of the domes constructed in this system.